The following data have been obtained for the effect of solvent composition on t

Question

The following data have been obtained for the effect of solvent composition on the solubility of a serine, an amino acid, at 10.0°C:

The data were obtained by mixing known volumes of methanol and water to obtain the desired solvent compositions, and then slowly adding measured amounts of serine to each mixture until no more would go into solution. The temperature was held constant at 10.0°C.

(a) Derive an expression for solvent composition expressed as mass fraction of methanol, x, as a function of volume fraction of methanol, f .
(b) Prepare a table of solubility of serine (g serine/g solution) versus mass fraction of methanol.

Volume % Methanol 0 10 20 30 40 60 80 100 Solubility (g/100 mL solvent)
22 22.72

18.98

11.58
6.415

4.205
1.805
.85 .65 Solution Density (g/mL)
1.00 .98 .97 .95 .94 .91 .88 .79

Explanation / Answer

(a) lets say mass and volume fraction of methanol are fm and fv respectively

lets say mass and volume of methanol Mm and Vm whereas mass and volume of water are Mw and Vw respectively

fm can be expressed as fm = Mm/(Mm+Mw)

= dmVm/(dmVm+dwVw)

whereas dm and dw are the density of methanol and water

Now fv = Vm/V

so fm become fm = dm. fv.V/dm.fvV+ dw(1-fv)V

this equation relates mass fraction with volume fraction of methanol

Mass Fraction of methanol Solubility of serine (g/g) 0 0.227 0.08 0.192 0.165 0.119 0.2534 0.067 0.3456 0.0446 0.5429 0.0197 0.76 0.0096 1 0.0082

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